A new approach for optical meta-lenses

Metamaterials are finding increasingly varied use in optics, acoustics, heat flow, mechanical engineering, and more. That's because their response to a given wavelength can be customized through tailoring the size, shape, and arrangement of their constituent subwavelength building blocks. (See the article by Martin Wegener and Stefan Linden, Physics Today, October 2010, page 32.) Although the parts are small, some applications may call for a metamaterial structure to be large. That can present quite a computational challenge: determining the optimal size, shape, and position of each component. Even a millimeter-diameter lens, for example, might contain upwards of a billion nanopillars. Steve Byrnes, Federico Capasso, and colleagues report a new strategy that greatly simplifies meta-lens design. The traditional approach starts with a regular arrangement of components and seeks to optimize their shape or size (as seen in the left-hand panel of the figure) for the desired lensing. That method works well near the center of the lens but can falter toward the periphery, particularly when the lens's numerical aperture is large. The researchers instead exploit the lens's symmetry in their calculations by dividing the lens into narrow rings and each ring into wedges. Except near the lens center, each wedge is sufficiently rectangular that calculations of the nanopillar shapes and positions in a given cell introduce little error when periodic boundary conditions are assumed. The results can be applied to other cells in the same ring and easily adjusted for adjacent rings (see the right-hand panel). The team demonstrated its approach by designing various lenses, including one that could focus yellow light while letting blue light pass through unrefracted. (S. J. Byrnes et al., Opt. Express 24, 5110, 2016.)